[Trevor]

"David" wrote in message
...
"William Sommerwerck" wrote in message ...

But by not switching doors, you are ignoring the new information that the
prize has to be behind one of the other two doors....

No, it doesn't. That's not correct.

You are sticking with
your original guess that had only a 1/3 chance of being right. By
switching
doors, you are including the new information that the prize has to be
behind
one of the other two doors, and your new chance of winning is 50%.

No, it doesn't. Your new chance of winning is 2/3.

***
This is similar to another puzzle. A couple has two children. What is the
probability that the second is a boy? The couple then volunteers that they
are not both girls. Now what is the probability the second is a boy?

The first case is 1/2. The second case is 2/3.


Wrong, on a purely statistical basis the first case is 50:50, BB, BG, GB, or
GG. Two out of four meet the criteria.
The second case is 50:50 Boy or Girl, One out of two meets the criteria.

However IF you know the average family statistics for your Country/town, you
can change those odds because you have more data. *If* the number of two
children families with 2 boys Vs 2 girls is known, one simply substitutes
the known data. It will probably be still close to 50:50 however in most
areas AFAIK.

Trevor.